Mathématiques

Question

Bonjour aidez-moi s’il vous plaît :

Factoriser chaque expression (grâce à une égalité remarquable ou un facteur commun):

A=x²-16=
B = 100+100x + 25x² =
C=14xy-21y =
D = 49x²-14x+1=
F = 3a²+ 6a =
G=4-121x² =
H = 64-121y² =
I=14x-21y+42 =
J = 9x² +24x+16=
K=5y²-y=
L = 4x² +25-20x =
M = 1- x² =

1 Réponse

  • Bonjour,

    A = x² - 16 = x² - 4² = (x - 4) (x + 4)

    B = 100 + 100x + 25x² = (5x)² + 2 × 5x × 10 + 10² = (5x + 10)²

    C = 14 xy - 21 y = 7y (2x - 3)

    D = 49x² - 14x + 1 = (7x)² - 2 × 7x × 1 + 1² = (7x - 1)²

    F = 3a² + 6a = 3a (a + 2)

    G = 4 - 121x² = 2² - (11x)² = (2 - 11x) (2 + 11x)

    H = 64 - 121y² = 8² - (11y)² = (8 - 11y) (8 + 11y)

    I = 14x - 21y + 42 = 7 (2x - 3y + 6)

    J = 9x² + 24x + 16 = (3x)² + 2 × 3x × 4 + 4² = (3x + 4)²

    K = 5y² - y = y (5y - 1)

    L = 4x² + 25 - 20x = (2x)² - 2 × 2x × 5 + 5² = (2x - 5)²

    M = 1 - x² = 1² - x² = (1 - x) (1 + x)

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